Title: |
Mathematics 721: Abstract Algebra II |
Credits: |
3 credits |
Prerequesites: |
Mathematics 720 or equivalent and/or consent of instructor |
Required for: |
Mathematics 724-725 |
Suggested Texts: |
Algebra Thomasa W. Hungerford Basic Algebra II Nathan Jacobson Algebra Serge Lang |
Supplemental Texts: |
Introduction to Commutative Algebra Michael Atiyah and Ian
G. MacDonald Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis and Irving Reiner Methods of Representation Theory, Volume I Charles W. Curtis and Irving Reiner Algebra: Rings, Modules, and Categories I Carl Faith Algebra II: Ring Theory Carl Faith Geometry of Coxeter Gropus Howard Hiller Category Theory Howard Hiller and George E. Streckler Noncommutative Rings Israel Herstein Algebraic Number Theory Serge Lang Categories for the Working Mathematician Saunders MacLane Theory of Categories Barry Mitchell Representations of Finite Groups Jean-Pierre Serre Algebra, Volume II Bartel L. van der Waerden Commutative Algebra, Volumes I & II Oscar Zariski and Pierre Samuel |
Graduate level survey of algebra: groups, rings, fields, Galois theory, and selected advanced topics.
| Morphisms, objects, and categories |
| Functors and natural transformations |
| Equivalence and isomorphism of categories |
| Limits and colimits |
| Representable functors, universals, and adjoint functors |
| Short exact sequences |
| Artinian and Notherian Modules |
| Tensor Product |
| Projective, Flat, and Injective Modules |
This course commences the "advanced" theory of algebraic structures through the introduction of the language of categories. MOdule categroies play and central role in the contemporary theory of rings and will enable us to continue the investigations initiated in Mathematics 720 at a higher and broader level.
The instructor can complete the course by the investigation of topics of the instructor's choice.